L-Functions and Automorphic Forms Conference, May 16 - 19, 2002, The Johns Hopkins University

Zeta函数和L函数为研究数论中的难点和基本问题提供了一个极其有力的方法。此外，类似的函数也出现在数学和物理学的其他部分，例如，提供看似发散的数据的正则化。自同构形的动态场是重要的Zeta函数的极好来源，事实上，朗兰兹的一个深远的猜想说，所有允许Euler积的Zeta函数都是模函数，即与GL(N)上的自同构形相关。这次会议将回顾和检验过去几年来取得的积极成果和技术，特别关注导致自同构形式从一组转移到另一组的各种情况的L函数方法。该奖项部分支持了数论会议。数论是研究数的性质的数学分支，例如素数的分布。这个特别的会议聚焦于某些类型的连续函数，称为自同构函数，它们编码了自然界中出现的深对称性，类似于小池塘上的波形。出现的离散音调具有有趣的数论意义。数学家和物理学家可以从离散的数字集合开始，并从这些数字构造连续函数开始，而不是从函数开始并寻找它们的离散色调。那么中心问题就是知道这些函数是否允许隐藏的对称性。当他们这样做的时候，那么更多的特殊性质也一定会出现。利用这类信息是一项紧迫的努力，还有许多金矿有待发现。

Zeta and L-functions provide an extremely powerful method for studying difficult and fundamental problems in Number theory. Moreover, analogous functions are propping up in other parts of Mathematics as well as inPhysics, for example to provide regularizations of seemingly divergent data.The dynamic field of Automorphic Forms is an excellent source of important zeta functions, and in fact a far-reaching conjecture of Langlands says that all zeta functions admitting an Euler product are modular, i.e., associated to automorphic forms on GL(n). This conference will review and examine the positive results and techniques which have come about in the past few years, with a special eye towards the L-function methods leading to various instances of transfer of automorphic forms from one group to another.This award partially supports a conference in number theory. Number theory is that branch of mathematics that studies properties of numbers, such as the distribution of prime numbers. This particular conference focuses on certain types of continuous functions, called automorphic functions, that encode deep symmetries which occur in nature, analogous to waveforms on a small pond. The discrete tones which occur have interesting number theoretic meanings. Instead of starting with the functions and looking for their discrete tones, mathematicians and physicists can start with discrete collections of numbers and from which they construct continuous functions. Then the central problem is to know if these functions admit hidden symmetries. When they do, then still more special properties must be present as well. Exploiting this kind of information is a pressing endeavor and there are many gold mines yet to be discovered.